In this form the dependence on \(F_E\)  is somewhat unwieldy.
When \(F_E\)  is diagonalizable, it is orthogonally so
[1]}, such that a transformation \(Q\)  exists, with \(Q^TQ=\mathbb {1}\) 
and \(Q^T F_E\, Q = \mathrm {diag}(\lambda _1,-\lambda _1, \lambda _2,-\lambda _2)\) ,
where
\(\lambda _{1,2} =& \tfrac{1}{2} \sqrt{f_1\mp \sqrt{f_1^2+16f_2^2}}.\) 
